Optimal Constellation Mapping for Pulse Amplitude Modulation Based Vertical Physical-Layer Network Coding

This paper discusses the denoise-and-forward (DNF) problem in two-way relay channel (TWRC). A pulse amplitude modulation (PAM) based vertical physical-layer network coding (VPNC) scheme is proposed and the optimal constellation mapping is studied to minimize the bit error rate (BER) and symbol error rate (SER) performance. Compared with the existing PNC scheme in which the relay superimposes two users´ signals of the same constellation, two users in the proposed VPNC scheme transmit PAM signals with vertical constellation and the relay superimposes two signals of vertical constellation. The closed form BER and SER expressions of the proposed VPNC scheme are also derived in this paper. Simulation results agree well with the theoretical analyses. Meanwhile, simulation results show that the proposed VPNC scheme outperforms the conventional PNC scheme on the SER and BER performance and optimal constellation mapping can obtain a about 1dB performance gain.